One morning in the fall of 1971, President Richard Nixon set out to fire J. Edgar Hoover, the director of the F.B.I., who had ruled over the agency like a potentate since 1924. The two men were longtime friends, united by their political affinities, including a bone-deep antipathy to the American left, Old and New, and a tendency to demonize their critics. Over the years, Nixon and his wife, Pat, had socialized often with Hoover and his companion, Clyde Tolson. They had even vacationed together in the fifties, at a seaside resort in La Jolla, California, owned by a pair of Texas oil tycoons who went out of their way to put their powerful guests at ease. After Nixon lost the 1960 Presidential election, to John F. Kennedy, Hoover was frankly disappointed, and wrote to urge his friend not to give up on politics: “The United States and the Free World need a man of your stature desperately.” When Nixon made his comeback, in 1968, Hoover was a distinct asset, an old-school embodiment of law and order for a Presidential campaign that presented itself as the antidote to urban uprisings, campus protests, and street crime.

But by that fall, more than two years into Nixon’s Presidency, Hoover had become a liability, the historian Beverly Gage explains in her crisply written, prodigiously researched, and frequently astonishing new biography, “G-Man: J. Edgar Hoover and the Making of the American Century” (Viking). He was seventy-six, and showing his age, napping for hours in his office in the afternoons. He was also showing, in Gage’s words, “increasing levels of vitriol and instability,” informing the White House, for instance, that the four student demonstrators shot to death by National Guardsmen at Kent State had “invited and got what they deserved.” In 1970, for the first time in a career in which he had enjoyed remarkable levels of public approval, half of Americans polled by Gallup said that they thought he should retire. And there was worse to come.

On the night of March 8, 1971, burglars broke into an F.B.I. field office in Media, Pennsylvania, and made off with a cache of top-secret files. The culprits, whose identities would not be revealed for years, were a small band of Quaker-inspired pacifists who suspected that the F.B.I. had infiltrated the antiwar movement and other New Left activities. They were proved right by the documents, which they pored over and then began releasing in tranches to two members of Congress, Senator George McGovern, of South Dakota, and Representative Parren Mitchell, of Maryland, and to three newspapers, the Los Angeles Times, the Washington Post, and the New York Times. (McGovern, Mitchell, and the L.A. Times turned the files over to the F.B.I.; the Post and, later, the Times chose to report on their contents.) Hoover’s F.B.I., as the files established, had engineered a clandestine campaign aimed at “disrupting” and “neutralizing” left-wing and civil-rights organizations through the use of informants, smear campaigns, and callous, cunning plots to break up marriages, get people fired, and exacerbate political divisions. One of the files made reference to the name of the project: cointelpro, which stood for “counterintelligence program.” It would take years of digging by journalists, reams of Freedom of Information Act requests, and the dogged work of the Church committee—a congressional body, chaired by the Idaho senator Frank Church, that was formed in 1975 to look into the nation’s intelligence activities—to reveal substantially more about the program. Under its auspices, the F.B.I. had wiretapped Martin Luther King, Jr.,’s hotel rooms and recorded his sexual assignations. In 1964, soon after King was awarded the Nobel Peace Prize, a package containing the tapes arrived at his home. His wife, Coretta Scott King, opened it. Inside was a letter, concocted by the F.B.I. and purporting to be from a disappointed Black supporter of King’s, that called him “a filthy, abnormal animal” while seemingly urging him to kill himself. cointelpro operatives went on to spread a false rumor that the actress Jean Seberg was pregnant by a member of the Black Panthers. (In fact, she was married and pregnant with her husband’s child, but, after the rumor circulated, she gave birth prematurely and lost the baby.) In 1969, cointelpro operatives collaborated with Chicago police in the raid that killed the twenty-one-year-old Black Panther leader Fred Hampton in his bed. Hoover, Gage notes, approved a bonus for the F.B.I. informant who had drawn a map of Hampton’s apartment, including where he slept.

In the outcry that followed the early revelations about cointelpro, some members of Congress called for Hoover’s resignation. Life ran an ominous image of him as a marble bust, with the cover line “Emperor of the F.B.I.” Even Nixon’s adviser Patrick Buchanan told the President that Hoover should go, before his reputation was picked over “by the jackals of the Left.” Amid public criticism, Hoover had—to Nixon’s annoyance—become uncharacteristically cautious on certain fronts. He was less aggressive than Nixon wanted him to be, for instance, in pursuing whoever had leaked the Pentagon Papers. In frustration, Nixon secretly authorized the creation of a team of intelligence operatives who would do whatever, in his view, had to be done. The team came to include a former F.B.I. agent, G. Gordon Liddy, and was code-named the Plumbers.

All that remained was to cut Hoover loose. The trouble was that he had no intention of leaving. He had already finagled an extension of the mandatory federal-government retirement age of seventy. By temperament and by ideology, he was inclined to hold on to his power in perpetuity. The President and his staff spent months scheming about how, exactly, to maneuver him out. They considered various deal sweeteners—including the idea of appointing Hoover to the Supreme Court. Nixon’s advisers composed a script for the President to use at a breakfast meeting with Hoover that morning in 1971, in which he would be assured that, if he stepped down, he would leave with “full honors (medal, dinner etc.).” The two men spoke for almost an hour at the White House, Gage tells us. But, in the end, Nixon could not bring himself to recite the script.